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Global Carleman Estimates for Waves and Applications [PDF]
Communications in Partial Differential Equations, 2013 31 ...
Lucie Baudouin, Maya de Buhan
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2017
In this monograph, we discuss the derivation of Carleman estimates and their application to inverse problems of determining spatially varying coefficients or source terms. The inverse problem is to determine unknown quantities in governing equations from available data of solutions.
Bellassoued M., Yamamoto M.
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In this monograph, we discuss the derivation of Carleman estimates and their application to inverse problems of determining spatially varying coefficients or source terms. The inverse problem is to determine unknown quantities in governing equations from available data of solutions.
Bellassoued M., Yamamoto M.
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Carleman Estimates for a Class of Degenerate Parabolic Operators [PDF]
SIAM Journal on Control and Optimization, 2008 Given $\alpha \in [0,2)$ and $f \in L^2 ((0,T)\times(0,1))$, we derive new Carleman estimates for the degenerate parabolic problem $w_t + (x^\alpha w_x) _x =f$, where $(t,x) \in (0,T) \times (0,1)$, associated to the boundary conditions $w(t,1)=0$ and $w(t,0)=0$ if $0 \leq \alpha
Piermarco Cannarsa
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Inverse problems and Carleman estimates
Inverse Problems, 1992The author describes the current state of the method of Carleman type estimates suggested by \textit{A. L. Bukhgejm} and himself [Dokl. Akad. Nauk SSSR 260, 269-272 (1981; Zbl 0497.35082)]. This method is based on powerful estimates of solutions of PDE in weighted Sobolev spaces which are a classical tool in the uniqueness of continuation study as well
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Carleman Estimates of Refined Stochastic Beam Equations and Applications
SIAM Journal on Control and Optimization, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yongyi Yu, Ji-Feng Zhang
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Carleman Estimates for Some Thermoelasticity Systems
2017In this chapter, we establish Carleman estimates for a thermoelastic plate system and a thermoelastic system with residual stress as applications of the Carleman estimate in Chap. 4.
Bellassoued M., Yamamoto M.
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Carleman Estimate for a Hyperbolic-Parabolic System
Differential Equations, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Carleman Estimates for Second-Order Hyperbolic Equations
Siberian Mathematical Journal, 2006Summary: In the space of variables \((x,t)\in\mathbb R^{n+1}\), we consider a linear second-order hyperbolic equation with coefficients depending only on \(x\). Given a domain \(D\subset\mathbb R^{n+1}\) whose projection to the \(x\)-space is a compact domain \(\Omega\), we consider the question of construction of a stability estimate for a solution to
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On Carleman estimates for hyperbolic equations
Asymptotic Analysis, 2002We prove a Carleman inequality for the second order hyperbolic equation in the cylinder Q with the norm of rightâhand side taken in the space (W12(Q))*.
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GLOBAL CARLEMAN ESTIMATES FOR DEGENERATE PARABOLIC OPERATORS WITH APPLICATIONS
Memoirs of the American Mathematical Society, 2016Degenerate parabolic operators have received increasing attention in recent years because they are associated with both important theoretical analysis, such as stochastic diffusion processes, and interesting applications to engineering, physics, biology, and economics.
Cannarsa, Piermarco +2 more
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